Adv Alg_Pract_Final Exam Review PART 2

Front

What is the empirical rule in statistics?

Back

The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

Front

What is a logarithm?

Back

A logarithm is the inverse operation to exponentiation, indicating the power to which a base must be raised to produce a given number. For example, log_b(a) = c means b^c = a.

Front

How do you convert radians to degrees?

Back

To convert radians to degrees, multiply the radian measure by 180/π. For example, 5π/6 radians = (5π/6) * (180/π) = 150°.

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output for each input from its domain. It can be represented as f(x).

Front

What is the difference between a linear function and a quadratic function?

Back

A linear function has the form f(x) = mx + b, where m and b are constants, and its graph is a straight line. A quadratic function has the form f(x) = ax^2 + bx + c, where a, b, and c are constants, and its graph is a parabola.

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval if, for any two points x1 and x2 in that interval, if x1 < x2, then f(x1) < f(x2).

Front

What is the definition of a factor in algebra?

Back

A factor is a number or expression that divides another number or expression evenly, without leaving a remainder.

Front

What is the relationship between logarithms and exponents?

Back

Logarithms and exponents are inverse operations. If b^y = x, then log_b(x) = y.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.